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The nonlinear distortion in single and multimode vertical-cavity surface-emitting lasers (VCSELs) under analog modulation was studied both numerically and experimentally. A quasi-three-dimensional time domain model was used to simulate the second-order harmonic and third-order intermodulation distortion in typical GaAs-based oxide-confined VCSELs emitting at 850 nm. The model is based on fundamental interrelated physical processes involving the optical fields and carrier and temperature distributions with no parameter fitting to experimental results. The simulations show that for low modulation frequencies (<2 GHz), the distortion is strongly affected by spatial hole burning, and at higher modulation frequencies, the distortion is dominated by the relaxation oscillation effects. At intermediate frequencies the two effects often cancel, resulting in a significantly lower distortion. Due to mode competition, the multimode VCSEL shows a more unpredictable behavior in the low frequency region. Moreover, in this region, the distortion of an individual mode can be much higher than the distortion of the total output power demonstrating the importance of avoiding mode-selective losses in multimode applications. The general trends observed in the simulations are well reproduced in the experiments.